A semi-analytic model for effects of fuzzy dark matter granule perturbations on orbital motion

In fuzzy dark matter scenarios, the quantum wave nature of ultralight axion-like particles generates stochastic density fluctuations inside dark matter haloes. These fluctuations, known as granules, perturb the orbits of subhaloes and other orbiting bodies. While previous studies have simulated these effects using N-body techniques or modelled them statistically using diffusion approximations, we propose an alternative framework based on representing the perturbations as a Fourier series with random coefficients, which can be applied to individual orbits, not just populations. We extend the model to finite-size subhaloes, identifying a critical length scale below which subhaloes behave as point-mass particles. In contrast, larger subhaloes exhibit suppressed perturbations from granules due to their extended mass profiles. Using FDM-Simulator, we validate our finite-size model by isolating granule accelerations and confirming their statistical effects on subhalo dynamics.